Luckily, some of the more well-informed Redditors shared their knowledge:

"A "redhead" is their stupid coffee :( I got all excited when I saw the sign thinking it was a red, spicy buffalo sandwich (or a real redhead which I would have preferred ;) ) But it is just coffee :("

And now we know.

On Wendy's end, it shows a disconnect in its marketing. Something like the Redhead, which obviously isn't a commonly known brand, needs a bit of context.